Sure, you can do that if you want or have to, but you won't be able to do it consistently or properly - you simply have to accept that some of your transliterations will be different than the official/proper transliterations of the same names, that the some of these people will have an official ID in Latin alphabet with a different name than what you wrote. And this is not a theoretical situation, such issues with wrong transliterations (and somebody missing a name because they're searching for a different spelling, or someone being offended because you wrote their name wrong) tend to appear ocasionally in various international sporting events, law enforcement and medicine/casualty situations.
There are no "official/proper transliterations" other than the ones you create for your institution, which is probably an academic library because I've not heard of anyone else caring about consistent transliteration. I've seen the same Greek and Russian names transcribed in all sorts of ways in government documents. Fortunately, all government documents have some kind of a number on them. That's what you use for your database key. Names aren't unique in any case, even with the extra variation introduced by whimsical transcription.
